Seminar Details
2013-04-30 (14.00) : Computing tensor decompositions with complex and polynomial optimization
At Euler building
Organized by Mathematical Engineering
Speaker :
Laurent Sorber (KULeuven)
Abstract :
Nonlinear optimization problems in complex variables are frequently encountered in applied mathematics and engineering applications. Tensor decompositions such as the canonical polyadic decomposition are examples of nonlinear optimization problems in several, possibly complex, variables. We give an introduction to tensors and tensor decompositions, their applications and how they can be computed with complex optimization. An important aspect of (complex) optimization are the underlying line and plane search (trust-region) subproblems. We show that in the context of tensor optimization, these subproblems are equivalent to solving a (possibly polyanalytic) polynomial system and develop a robust method of solving such systems with a single generalized eigenvalue decomposition. Finally, algorithms are demonstrated using our recently published MATLAB toolbox Tensorlab.